Solve a^2div7*5=13*0.67

$$a ^ { 2 } \div 7 \cdot 5 = 13 \cdot 0.67$$

Solve for a

$$a = \frac{\sqrt{30485}}{50} \approx 3.491990836$$

$$a = -\frac{\sqrt{30485}}{50} \approx -3.491990836$$

Steps by Finding Square Root

Multiply both sides of the equation by 7.

$$a^{2}\times 5=91\times 0.67$$

Multiply 91 and 0.67 to get 60.97.

$$a^{2}\times 5=60.97$$

Divide both sides by 5.

$$a^{2}=\frac{60.97}{5}$$

Expand \frac{60.97}{5} by multiplying both numerator and the denominator by 100.

$$a^{2}=\frac{6097}{500}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{30485}}{50} a=-\frac{\sqrt{30485}}{50}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 7.

$$a^{2}\times 5=91\times 0.67$$

Multiply 91 and 0.67 to get 60.97.

$$a^{2}\times 5=60.97$$

Subtract 60.97 from both sides.

$$a^{2}\times 5-60.97=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$5a^{2}-60.97=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -60.97 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 5\left(-60.97\right)}}{2\times 5}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 5\left(-60.97\right)}}{2\times 5}$$

Multiply -4 times 5.

$$a=\frac{0±\sqrt{-20\left(-60.97\right)}}{2\times 5}$$

Multiply -20 times -60.97.

$$a=\frac{0±\sqrt{1219.4}}{2\times 5}$$

Take the square root of 1219.4.

$$a=\frac{0±\frac{\sqrt{30485}}{5}}{2\times 5}$$

Multiply 2 times 5.

$$a=\frac{0±\frac{\sqrt{30485}}{5}}{10}$$

Now solve the equation a=\frac{0±\frac{\sqrt{30485}}{5}}{10} when ± is plus.

$$a=\frac{\sqrt{30485}}{50}$$

Now solve the equation a=\frac{0±\frac{\sqrt{30485}}{5}}{10} when ± is minus.

$$a=-\frac{\sqrt{30485}}{50}$$

The equation is now solved.

$$a=\frac{\sqrt{30485}}{50} a=-\frac{\sqrt{30485}}{50}$$